My take on Dr. Manhattan has always been that Moore's point with the character was that if such a being were to come into existence, that they would ultimately not become an altruistic superhero like Superman, regardless of intentions. Dr. Manhattan essentially lost his humanity, and eventually left Earth and humanity behind. Watchmen has always been about deconstructing the idea of superheroes, and Dr. Manhattan is the "what if" of actually having extraordinary powers.
In the HBO Watchmen, the human characters such as Will Reeves and Lady Trieu comment about how Dr. Manhattan did not do enough, given the powers that he had. Lady Trieu intended to give herself Dr. Manhattan's abilities so that she could use them to save the world in all the ways that Dr. Manhattan never did. Of course, her motivations were completely narcissistic rather than altruistic, but I still think that suddenly gaining such superpowers would inevitably change the character similarly to Dr. Manhattan.
So, what could be done with Angela is to play out the scenario where she suddenly finds herself with the superpowers, and despite being the good character that was established in season one, she finds herself slipping down that same path. Despite pressure from her grandfather to do a lot more with her powers to make the world better, like Dr. Manhattan never really did, she finds out all the reasons why Dr. Manhattan never did. We would get to see her coming to terms with the realities of her deceased husband's situation, that she could never previously understand. I would have no problem with this ultimately leading the character down the same path as Dr. Manhattan, and eventually losing touch with her own humanity. Everybody wants to believe that they would do amazing things with such powers, but the reality of it is simply beyond human comprehension, and that's the whole point.
For a second season of the show, I would not center it around Angela as the main character. I would shift the focus to human characters, because Angela is no longer human. Dan Dreiberg could be explored, flashing back to how he ended up in prison, while Laurie ended up becoming a hunter of masked heroes for the FBI. It could follow through in the present with bringing Veidt to justice, and all that would imply for Laurie and Dan for their involvement, having known the truth all along. Perhaps Angela, finally understanding the realities of Dr. Manhattan's powers, can intervene and shine a new light on the situation.
Perhaps a good way to tie the entire thing up would be for Angela to ultimately undo the events that caused the Watchmen universe to diverge from the real-world history that we all know, restoring the history that we do know, with implications to all the various characters. I think that could be the way to deconstruct Watchmen, like Watchmen deconstructs the concept of superheroes. End it with Angela enjoying a family Christmas, in Tulsa, where she has always lived, with her parents and grandparents alive, married to the original Cal, with children of their own, nobody the wiser to the alternate reality where masked heroes and people with god-like powers screwed everything up.
However, the entire season leading up to such an ending could be free to explore an even more screwed up history, taken to whatever extreme might cause Angela to ultimately undo it all.
Or, instead of re-aligning the Watchmen universe with our own, it ends up creating an alternate history that is better than our reality. Maybe this new reality never became the socially divisive world that we currently know, where everybody has gone to political extremes, and can't enjoy Star Wars and Star Trek anymore without all the hate and vitriol. Maybe modern movies and television don't suck so bad in this reality, because art imitates life, leaving us to realize that we are all part of the problem that got us to the dismal reality that we currently know and complain about on the internet.
Crazy as it may sound, I think that would actually be in the spirit of Alan Moore's intentions with the original graphic novel. Humans are going to be humans, and fantasies about superheroes are unrealistic, and ultimately just a reflection of human psychology and history. Watchmen is about showing the "what if", and showing that it would not be like in the traditional superhero stories, with truth and justice for all, and good triumphing over evil. Our world didn't need such characters to prevent humanity from destroying itself in nuclear Armageddon, but humanity still finds plenty of other ways to screw the world up anyway. We're all just slightly less "dumb" apes, lost in our contrived sense of intelligent superiority and mastery of our own world.
While I would actually be perfectly satisfied to let the HBO Watchmen stand alone as the single season, I think there is plenty left to be explored, and plenty that could be compelling about it moving forward for another season or two. Just playing devil's advocate here.